Thousands of uninsured Massachusetts workers in low-wage jobs are ineligible for state-subsidized health coverage, but they will qualify for these low-cost plans under the new national health care overhaul — in 2014.

Now, some consumer advocates, arguing that the wait is unfair and a black eye for the state, want the Patrick administration and legislators to launch a program to cover at least part of this group. Administration officials, already facing huge budget deficits, say the state can’t afford the tens of millions of dollars it would cost to subsidize additional workers’ insurance.

The state’s landmark 2006 health insurance law was a model for the national legislation passed in March and has reduced the percentage of uninsured to under 4 percent of adults. But it did little for full-time workers whose employer offers health insurance they cannot afford. The law bars them from getting lower-priced coverage through the state, even if their pay is below levels that would otherwise make them eligible for state assistance.

“The federal law learned from our experience, both good and bad, and saw this as a deficiency in health reform,’’ said Brian Rosman, research director for the Boston-based consumer group Health Care for All. “It’s not that they just copied what worked here. They also saw things that maybe didn’t work and fixed it.’’

The state doesn’t track how many uninsured work for companies that offer coverage, but the Urban Institute, a Washington-based think tank, estimates that as of last fall, there were 15,000 to 50,000 such people.

Among them is Karen Cifuentesof Lynn, who said “it’s really unfair’’ that she will have to wait for low-cost coverage. She makes $11.50 an hour working full time as a receptionist at a car dealership, in addition to taking night college classes. By the time she pays the $450 monthly day-care bill for her 3-year-old daughter, plus a car loan and car insurance, there is little left over to afford the $150 monthly premium for health insurance at work, she said. So she goes without coverage, and tries not to get sick because she can’t afford that, either.

“I am glad I was offered a full-time position. Not many people have jobs,’’ Cifuentes said. “But no matter how hard I try . . . I can’t afford health insurance.’’

Under the state law, adults whose employers don’t offer coverage or who are out of work are eligible for state assistance with health insurance if they make less than three times the federal poverty level — which translates to $43,710 for a family of two, such as Cifuentes and her daughter. Cifuentes earns about $24,000.

The law was designed to encourage employers to offer health insurance and workers to buy that coverage, and it imposes tax penalties on most who don’t comply.

Workers whose employers offer a health plan were blocked from state assistance because the law’s architects worried that too many companies and employees would drop that coverage, if low-income workers were allowed to get cheaper insurance through the Connector, the program that provides subsidized coverage.

But Health Care for All said many of the 3,500 monthly calls to its Helpline are from low-income workers who can’t afford their insurance.

The group proposed a pilot program that would offer access to state insurance for those who earn no more than one and a half times the federal poverty level. State numbers indicate that would extend eligibility to about 150,000 low-income workers, though it is not known how many of them would actually apply for the state assistance.

Even under that proposal, Cifuentes would just miss qualifying, making about $2,000 more than would be allowed.

Connector Authority spokesman Richard Powers said state regulators had intended to evaluate a potential pilot program in 2008, but then the recession hit, and everything was put on hold.

“Our focus turned from expansion to preservation,’’ he said, “and we are still in that mode today.’’

The Connector did not specifically estimate the cost of a pilot program, but officials believe the costs could escalate quickly because currently insured workers would shift to the cheaper state plans. In a June 2008 report, the Connector estimated that extending subsidized coverage to 50,000 working adults would have cost the state $50 million in the last fiscal year, even if employers helped defray the cost.

In 2014, when Cifuentes and thousands of other Massachusetts residents will be eligible for Connector coverage, the bill will largely be paid with federal money.

Connector board member Celia Wcislo, who also is an assistant director of a large health care workers union, the 1199SEIU, said now that the economy is showing signs of picking up, the board should try a small pilot project to determine, among other things, how many workers who would be newly eligible for subsidized insurance would actually sign up.

“It would make sense to try a pilot now, to see what happens, and learn from it,’’ Wcislo said, “so we are ready by 2014 to open it up to everybody who is eligible.’’

In April, the Massachusetts Supreme Judicial Court upheld the state’s authority to deny subsidized coverage to these low-income workers, rejecting consumer advocates’ arguments that the 2006 law directed regulators to create a waiver program that would have helped at least some of these adults get state assistance.

Patti Prunhuber, a Worcester lawyer who unsuccessfully argued the case to the high court, said the Massachusetts law is flawed.

“Working poor people are penalized because they can’t afford to access their employer’s health insurance,’’ she said. “But if their hours were reduced so that they no longer qualified for employer health insurance, then they would be eligible.’’

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